Can I use a digital camera to make a short film?

Yes, but it is easier if you can control the sound better... Many domestic cameras are high enough quality these days but the reason pro's do not use them very often is because for decent quality you need to be able to attach external microphones to get good sound quality. The Jack film was shot on canon xm2's. If you are just in it for fun then go ahead and make whatever film you want on whatever you want, the practice is the important thing, if you want to win a competition or something then get a camera with external audio inputs. You can have a crappy image with good sound and it will seem higher quality than the same thing with a good image and crappy sound.